The Taylor series of e^(5x) about x = 0 has the coefficient of x³ equal to
Answer and explanation
Correct answer: C. 20.8
- Step 1: e^(ax) = Σ (ax)ⁿ/n!, so the x³ term is a³x³/3!. Step 2. The coefficient is 125/6 = 20.8. Answer: 20.8. Why not the others: 41.7 is what you get if you divide by 3 instead of 3!. 0.8 is what you get if you forget to cube a. 12.5 is what you get if you give the coefficient of x².
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